I'm not aware of any command to count the number of solutions. But this can be done easily using MathSAT's API. Create a counter, and increase it each time MathSAT notifies.
static int counter = 0;
static int my_callback(msat_term *model, int size, void *user_data)
{
counter++; return 1;
}
...
msat_all_sat(env, important, 4, my_callback, &data);